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arXiv:physics/0006066 · Physical Review A

Theory of coherent photoassociation of a Bose-Einstein condensate

Marijan Koštrun, Matt Mackie, Robin Côté, Juha Javanainen

Published Nov 15, 2000• 86 citations
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Abstract

We study coherent photoassociation, phenomena analogous to coherent optical transients in few-level systems, which may take place in photoassociation of an atomic Bose-Einstein condensate but not in a nondegenerate gas. We develop a second-quantized Hamiltonian to describe photoassociation, and apply the Hamiltonian both in the momentum representation and in the position representation (field theory). The solution of the two-mode problem, including only one mode each for the atomic and molecular condensates, displays analogs of Rabi oscillations and rapid adiabatic passage. A classical version of the field theory for atoms and molecules is used to demonstrate that, in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of density fluctuations. Experimental complications, including spontaneous emission and unwanted ``rogue'' photodissociation from a photoassociated molecule, are analyzed. A two-color Raman scheme is studied as a method to set up an effective two-mode scheme with reduced spontaneous-emission losses. We discuss photoassociation rates and photoassociation Rabi frequencies for high-lying vibrational states in alkali dimers both on the basis of molecular-structure calculations, and by comparing with an experiment [Wynar et al., Science 287, 1016 (2000)].

DOI
10.1103/physreva.62.063616

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STIMULATED RAMAN MOLECULE FORMATION IN COLD ALKALI GASES.

Paul S. Julienne, Keith R. Burnett, Y. B. Band +1 more

Photoassociation is a process by which two cold, trapped atoms can be optically excited during a collision to make a vibrational level of an excited electronic state of a molecular dimer. High-resolution photoassociation spectra are now well-known for most alkali dimers. The upper level normally decays by spontaneous emission to a number of final molecular levels, bound and unbound. A laser of a second color can be used to stimulate a transition from the upper level to a particular ground state vibrational level. Such a Raman photoassociation process can be used to form translationally cold molecules in a cold atomic gas or a Bose-Einstein condensate. Coupled channels scattering calculations show that the collisional rate coefficient for coherent production of molecules in specific target states, $> 10^{-10} cm^{3}/s,$ can greatly exceed the rate coefficient for forming products due to excited state spontaneous decay. This implies the feasibility of rapid coherent conversion of atom pairs in a condensate to molecules on a time scale short compared to the trap oscillation time. The untrapped molecules can form a coherent molecular beam. We will examine the prospects for the experimental realization of photoassociative molecule formation in cold alkali gases or condensates.

•Jan 1, 1998•0 citations
We study coherent photoassociation, phenomena analogous to coherent optical transients in few-level systems, which may take place in photoassociation of an atomic Bose-Einstein condensate but not in a nondegenerate gas. We develop a second-quantized Hamiltonian to describe photoassociation, and apply the Hamiltonian both in the momentum representation and in the position representation (field theory). The solution of the two-mode problem, including only one mode each for the atomic and molecular condensates, displays analogs of Rabi oscillations and rapid adiabatic passage. A classical version of the field theory for atoms and molecules is used to demonstrate that, in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of density fluctuations. Experimental complications, including spontaneous emission and unwanted ``rogue'' photodissociation from a photoassociated molecule, are analyzed. A two-color Raman scheme is studied as a method to set up an effective two-mode scheme with reduced spontaneous-emission losses. We discuss photoassociation rates and photoassociation Rabi frequencies for high-lying vibrational states in alkali dimers both on the basis of molecular-structure calculations, and by comparing with an experiment [Wynar et al., Science 287, 1016 (2000)].
A study of coherent photoassociation is presented for the case of an atomic Bose-Einstein condensate. It is shown that the phenomenon is analogous to coherent optical transient in a few-level system, with a difference that the participating levels have Bose enhanced populations. A second-quantized Hamiltonian in momentum and position representation is developed to describe photoassociation. A classical version of the field theory for atoms and molecules is used to demonstrate that in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of the density fluctuations. ^ A simple mean-field model of atom-molecule Bose-Einstein condensate is constructed and it is shown that in the model there is no collapse, irrespective of the sign of the effective atom-atom scattering length. The properties of the two most important eigenstates, the ground state and the twin state, are determined for different values of the system parameters δ and K, the detuning and the atom-molecule coupling, respectively. It is shown that in a coupled atom-molecule system a collapse is replaced by a dynamical instability. The lines in the parameter space where these instabilities occur are in fact fractures where the underlying eigenstates discontinuously change. The features of instability are in good qualitative agreement with the experimental observations of collapse. ^
We consider the process of photoassociation (PA) that occurs when a pair of colliding atoms interacts with a photon, thereby making a transition from the two-atom continuum to a bound molecular state. Such free-bound transitions are described by quantizing the molecule's dissociation continuum, and coupling each of these quasicontinuum (QC) levels to a similarly discrete molecular level. The correct free-atom results are recovered no later than at the end of a given calculation by taking the limit as the QC spacing tends to zero. From the quasicontinuum model, we are led to adapt the few-level and second-quantization methods of photon optics to analyze free-bound transitions. In particular, we establish the PA density parameter as nearly identical to the phase-space parameter as a Bose-Einstein condensate (BEC), illustrate the near-unit efficiency of one- and two-color photoassociation of a BEC, and develop coherent atom-molecule transitions as the matter optics version of second-harmonic generated photons. ^
We demonstrate coherent one-color photoassociation of a Bose-Einstein condensate, which results in Rabi oscillations between atomic and molecular condensates. We attain atom-molecule Rabi frequencies that are comparable to decoherence rates by driving photoassociation of atoms in an ^{88}Sr condensate to a weakly bound level of the metastable 1S0+3P1 molecular potential, which has a long lifetime and a large Franck-Condon overlap integral with the ground scattering state. Transient shifts and broadenings of the excitation spectrum are clearly seen at short times, and they create an asymmetric excitation profile that only displays Rabi oscillations for blue detuning from resonance.
We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found, and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett. 88, 090403 (2002)10.1103/PhysRevLett.88.090403], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms.
In this paper we formulate the time-dependent many-body theory of photoassociation in an atomic Bose-Einstein condensate with realistic interatomic interactions, using and comparing two approximations: the first-order cumulant approximation [Phys. Rev. A 65, 033601 (2002)], and the reduced pair wave approximation [Phys. Rev. A 68, 033612 (2003)]. The two approximations differ only by the way a pair of condensate atoms is influenced by the mean field at short interatomic separations. In both cases we identify two different regimes of photoassociation: the adiabatic regime and the coherent regime. The threshold for the so-called ``rogue dissociation'' [Phys. Rev. Lett. 88, 090403 (2002)] (where the Gross-Pitaevski\ifmmode \breve{\imath}\else \u{\i}\fi{} model breaks down) is found to be different in each regime, shedding new light on the experiment of McKenzie et al. [Phys. Rev. Lett. 88, 120403 (2002)]. Comparing numerical solutions for the two approximations with the Gross-Pitaevski\ifmmode \breve{\imath}\else \u{\i}\fi{} predictions, we find two different effects: reduction of the photoassociation rate at short times, and creation of correlated pairs of atoms when the laser intensity is switched on rapidly. We also observe effects on the symmetry of the photoassociation line shapes, giving the possibility to experimentally distinguish between the two approximations.
Photoassociation is a process by which two cold, trapped atoms can be optically excited during a collision to make a vibrational level of an excited electronic state of a molecular dimer. High-resolution photoassociation spectra are now well-known for most alkali dimers. The upper level normally decays by spontaneous emission to a number of final molecular levels, bound and unbound. A laser of a second color can be used to stimulate a transition from the upper level to a particular ground state vibrational level. Such a Raman photoassociation process can be used to form translationally cold molecules in a cold atomic gas or a Bose-Einstein condensate. Coupled channels scattering calculations show that the collisional rate coefficient for coherent production of molecules in specific target states, >10−10cm3/s,> 10^{-10} cm^{3}/s,>10−10cm3/s, can greatly exceed the rate coefficient for forming products due to excited state spontaneous decay. This implies the feasibility of rapid coherent conversion of atom pairs in a condensate to molecules on a time scale short compared to the trap oscillation time. The untrapped molecules can form a coherent molecular beam. We will examine the prospects for the experimental realization of photoassociative molecule formation in cold alkali gases or condensates.